Differential codebook for a wireless network, MIMO beamforming system using same, and method of reducing a quantization error in a MIMO beamforming system for a wireless network using same

ABSTRACT

A differential codebook for a wireless network includes a plurality of codewords and [e 1  . . . e N     s   ] G as a center location of the plurality of codewords, where e k  represents a column vector comprising a plurality of rows including a k-th row and in which an entry on the k-th row is one and entries on each of the plurality of rows except for the k-th row are zero, where G is any N s  by N s  unitary matrix including the identity matrix, and where N s , represents a number of spatial streams in the wireless network. At least two of the plurality of codewords are symmetric about the center location.

PRIORITY CLAIM

This application claims the benefit of priority under 35 U.S.C. §119(e) to U.S. Provisional Patent Application Ser. No. 61/156,882, filed Mar. 3, 2009, which is incorporated herein by reference in its entirety.

FIELD OF THE INVENTION

The disclosed embodiments of the invention relate generally to wireless communications, and relate more particularly to beamforming in wireless communication networks.

BACKGROUND OF THE INVENTION

In closed-loop multiple input/multiple output (MIMO) beamforming in a wireless network comprising a subscriber station and a base station, the subscriber station (also referred to at times herein as a mobile device or a receiver) quantizes the ideal beamforming matrix and sends a quantization index corresponding to the ideal beamforming matrix back to the base station (also referred to at times herein as a transmitter). The base station reconstructs the beamforming matrix according to the fed-back index and conducts the beamforming. It is well known that beamforming increases the link performance and system throughput.

The beamforming matrix can be fed back differentially. The change between the current beamforming matrix and the previous one can be quantized by a codebook and the corresponding quantization index can be fed back. The quantization codebook determines the beamforming accuracy and tracking capability.

Embodiments of the invention may find application in a wireless local area network (WLAN) or a wireless Metropolitan area network (WMAN) including a WiMAX (Worldwide Interoperability for Microwave Access) network or the like. WiMAX technology is based on the IEEE 802.16 family of standards, including IEEE 802.16e, IEEE 802.16m, and others.

BRIEF DESCRIPTION OF THE DRAWINGS

The disclosed embodiments will be better understood from a reading of the following detailed description, taken in conjunction with the accompanying figures in the drawings in which:

FIG. 1 is a stylized representation of a differential codebook according to an embodiment of the invention;

FIGS. 2 and 3 are depictions of quantization codebooks that make use of input symmetry according to embodiments of the invention;

FIG. 4 is a concise representation of orthogonal matrices on Grassmannian manifold according to an embodiment of the invention; and

FIG. 5 is a flowchart illustrating a method of reducing a quantization error in a MIMO beamforming system for a wireless network according to an embodiment of the invention.

For simplicity and clarity of illustration, the drawing figures illustrate the general manner of construction, and descriptions and details of well-known features and techniques may be omitted to avoid unnecessarily obscuring the discussion of the described embodiments of the invention. Additionally, elements in the drawing figures are not necessarily drawn to scale. For example, the dimensions of some of the elements in the figures may be exaggerated relative to other elements to help improve understanding of embodiments of the present invention. The same reference numerals in different figures denote the same elements, while similar reference numerals may, but do not necessarily, denote similar elements.

The terms “first,” “second,” “third,” “fourth,” and the like in the description and in the claims, if any, are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order. It is to be understood that the terms so used are interchangeable under appropriate circumstances such that the embodiments of the invention described herein are, for example, capable of operation in sequences other than those illustrated or otherwise described herein. Similarly, if a method is described herein as comprising a series of steps, the order of such steps as presented herein is not necessarily the only order in which such steps may be performed, and certain of the stated steps may possibly be omitted and/or certain other steps not described herein may possibly be added to the method. Furthermore, the terms “comprise,” “include,” “have,” and any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements is not necessarily limited to those elements, but may include other elements not expressly listed or inherent to such process, method, article, or apparatus.

The terms “left,” “right,” “front,” “back,” “top,” “bottom,” “over,” “under,” and the like in the description and in the claims, if any, are used for descriptive purposes and not necessarily for describing permanent relative positions. It is to be understood that the terms so used are interchangeable under appropriate circumstances such that the embodiments of the invention described herein are, for example, capable of operation in other orientations than those illustrated or otherwise described herein. The term “coupled,” as used herein, is defined as directly or indirectly connected in an electrical or non-electrical manner. Objects described herein as being “adjacent to” each other may be in physical contact with each other, in close proximity to each other, or in the same general region or area as each other, as appropriate for the context in which the phrase is used. Occurrences of the phrase “in one embodiment” herein do not necessarily all refer to the same embodiment.

DETAILED DESCRIPTION OF THE DRAWINGS

In many cases, the input to a quantization codebook is symmetric about a center [e₁ . . . e_(N) _(s) ]. The codebook may therefore be designed to make use of this symmetry, such as by selecting codeword locations in order to reduce quantization error. Accordingly, in at least one embodiment of the invention, a differential codebook for a wireless network comprises a plurality of codewords and [e₁ . . . e_(N) _(s) ] G as a center location of the plurality of codewords, where e_(k) represents a column vector comprising a plurality of rows including a k-th row and in which an entry on the k-th row is one and entries on each of the plurality of rows except for the k-th row are zero, where G is any N_(s) by N_(s) unitary matrix including the identity matrix, and where N_(s) represents a number of spatial streams in the wireless network. At least two of the plurality of codewords are symmetric about the center location. When G is the identity matrix, [e₁ . . . e_(N) _(s) ] G=[e₁ . . . e_(N) _(s) ].

Referring now to the drawings, FIG. 1 is a stylized representation of a differential codebook 100 according to an embodiment of the invention. The previous beamforming matrix {circumflex over (V)}(t−1) is known at both the transmitter and the receiver. The current beamforming matrix {circumflex over (V)}(t) needs to be quantized differentially with respect to {circumflex over (V)}(t−1). A quantization codebook is deployed around {circumflex over (V)}(t−1) so that one of the codewords may be close to {circumflex over (V)}(t). The index of the codeword closest to {circumflex over (V)}(t) is fed back to the transmitter.

A differential feedback scheme that may make use of differential codebook 100 and the concepts presented above is discussed in detail in U.S. application Ser. No. 12/584,142, which is hereby incorporated by reference herein in its entirety. For convenience, certain details of that exemplary differential feedback scheme are reproduced below.

Differential at subscriber station:

D=[{circumflex over (V)}(t−1){circumflex over (V)} ^(⊥)(t−1)]^(H) V(t).  (1)

Quantization at subscriber station:

$\begin{matrix} {\hat{D} = {\underset{D_{i} \in C_{d}}{\arg \; \max}{{{D^{H}D_{i}}}_{F}.}}} & (2) \end{matrix}$

Beamforming matrix reconstruction at base station:

{circumflex over (V)}(t)=[{circumflex over (V)}(t−1){circumflex over (V)} ^(⊥)(t−1)]{circumflex over (D)}.  (3)

Beamforming at base station:

y=H{circumflex over (V)}(t)s+n.  (4)

In (1), the N_(t)×N_(s), V(t) and {circumflex over (V)}(t) are, respectively, the ideal and quantized beamforming matrices for frame t, and {circumflex over (V)}^(⊥)(t−1) is N_(t)×(N_(t)−N_(s)) and has the complementary columns orthogonal to {circumflex over (V)}(t−1). N_(t) is the number of transmit antennas at the transmitter. In (2), the differential codebook C_(d) may be referred to as a polar cap. In (4), y is the received vector, H is the channel matrix of size N_(r)×N_(t) (where N_(r) is the number of receive antennas), {circumflex over (V)}(t) is the reconstructed beamforming matrix (or vector) of size N_(t) by N_(s), s is the N_(s)×1 data vector, and n is the complex additive white Gaussian noise plus interference.

In practice, (1) and (2), which are illustrative and which tend to degrade performance, are combined. The receiver maximizes the beamformed channel capacity (or another performance metric) by inserting each codeword into the expression of the testing beamformed channel capacity as

$\begin{matrix} {{\hat{D} = {\underset{D_{i} \in C_{d}}{\arg \; \max}\; {\det\left( {I + {\frac{\gamma}{N_{s}}D_{i}^{H}{Q\left( {t - 1} \right)}^{H}H^{H}{{HQ}\left( {t - 1} \right)}D_{i}}} \right)}}},} & (5) \end{matrix}$

where Q(t−1)=[{circumflex over (V)}(t−1) {circumflex over (V)}^(⊥)(t−1)]. Expression (5) may be simplified as

$\hat{D} = {\underset{D_{i} \in C_{d}}{\arg \; \max}{{{{H\left\lbrack {{\hat{V}\left( {t - 1} \right)}\mspace{14mu} {{\hat{V}}^{\bot}\left( {t - 1} \right)}} \right\rbrack}^{H}D_{i}}}^{2}.}}$

Since the most probable outcome is for {circumflex over (V)}(t) to remain the same as {circumflex over (V)}(t−1), the polar cap C_(d) should have the N_(t)×N_(s)

$\begin{bmatrix} 1 & \; & \; \\ \; & \ddots & \; \\ \; & \; & 1 \end{bmatrix} = \left\lbrack {e_{1}\ldots \mspace{14mu} e_{N_{s}}} \right\rbrack$

as a codeword so that {circumflex over (V)}(t) remains the same as {circumflex over (V)}(t−1) after the reconstruction in (3). Namely,

{circumflex over (V)}(t−1)=[{circumflex over (V)}(t−1){circumflex over (V)} ^(⊥)(t−1)][e ₁ . . . e _(N) _(s) ].  (6)

This allows the beamforming matrix to stay in the optimal point for low mobility channels. (Without the [e₁ . . . e_(N) _(s) ] codeword the codebook would tend to vibrate around the optimum point.) Furthermore, the locations of {circumflex over (V)}(t) are symmetric about {circumflex over (V)}(t−1). Therefore, besides the center codeword [e₁ . . . e_(N) _(s) ], the e remaining quantization codewords should be symmetric about [e₁ . . . e_(N) _(s) ].

One simple configuration is as follows. The remaining codewords have equal distance to the center. Note that all codeword are on the appropriate (including but not limited to Grassmannian, Stiefel) manifold. There are multiple definitions for the distance between two codewords, e.g., chordal distance and average channel capacity loss. For a low signal to noise ratio (SNR) region, the distance may be

d(A,B)=trace(A ^(H) BB ^(H) A),  (7)

where A and B are two N_(t)×N_(s), codewords. For other SNR regions, the distance may be

$\begin{matrix} {{{d\left( {A,B} \right)} = {\det\left( {I + {\frac{\gamma}{N_{s}}A^{H}{BB}^{H}A}} \right)}},} & (8) \end{matrix}$

where γ is the signal to noise ratio or a predetermined scalar. For simplicity, (8) may be simplified as

d(A,B)=det(A ^(H) BB ^(H) A)  (9)

The realization that the input to the quantization codebook is symmetric about a center [e₁ . . . e_(N) _(s) ] permits the design of a codebook that makes use of this symmetry. FIGS. 2 and 3 depict two such designs according to embodiments of the invention. Both of the depicted codebooks are designed to minimize quantization error.

FIG. 2 depicts a differential codebook 200 according to an embodiment of the invention. The center of differential codebook 200 is [e₁ . . . e_(N) _(s) ], but no codeword is located at the center. In this case, all the codewords are set around a center at [e₁ . . . e_(N) _(s) ]. This configuration may be desirable for at least the following two reasons. First, the distance between any two codewords may be greater than the distance between any codeword and the center [e₁ . . . e_(N) _(s) ]. In other words, the quantization error is greater outside the center than near the center. Therefore, no codeword is set on the center for reducing the large quantization error outside the center. Second, the beamforming matrix may tend to change substantially between adjacent feedbacks in some situations. Therefore, there is no need for the codeword [e₁ . . . e_(N) _(s) ] that keeps the beamforming matrix at the same place. The codewords have an equal distance d₀ to the center. The distance between any pair of codewords is d₁. This structure may be desirable when the number of codewords is not much greater than the degree of freedom of differential codebook 200 and the radius of the codebook is relatively large. For example, the differential codebook for tracking a 4×2 beamforming matrix has 7 degrees of freedom. If the distance between the codeword and the codebook center is 20 degrees and the number of codewords is 8, then differential codebook 200 may be desirable.

FIG. 3 depicts a differential codebook 300 according to an embodiment of the invention. Unlike differential codebook 200, differential codebook 300 has a center codeword. The distance from the center codeword to the other codewords is d₀. The non-center codewords are each equidistant from each other, having separation distance d₁, as illustrated.

The wireless network may define several differential codebooks with different sizes of d₀. The smaller d₀, the smaller the quantization error. Thus, in one embodiment, as further discussed below, a method of reducing a quantization error in a MIMO beamforming system comprises minimizing d₀, or in other words, constraining d₀ to be less than some predetermined limit. However, for small d₀, the feedback may not be able to track the fast variation of a beamforming matrix that may vary more than d₀ between two adjacent feedbacks. On the other hand, large d₀ tracks the channel variation well, but at the cost of greater quantization error.

In reality, the base station may select one of the differential codebooks according to, for example, its antenna configuration (or correlation) and the mobile speed. The index of the selected codebook may then be sent to the mobile station. Alternatively, the mobile station may select one of the differential codebooks based on, for example, the correlation (or variation) of the ideal beamforming matrix. For example, the mobile station may estimate the channel matrices from the mid-ambles and compute the ideal beamforming matrices. The variations of the beamforming matrix are also computed. Based on the variations, the mobile station selects one differential codebook and sends the corresponding codebook index to the base station.

Accordingly, certain embodiments of the invention involve a MIMO beamforming system for a wireless network that comprises a plurality of differential codebooks, each of which are similar to the differential codebook that was described earlier herein, i.e., each of which (among other characteristics) has a plurality of codewords and contains [e₁ . . . e_(N) _(s) ] G as a center location of the plurality of codewords, as has been described. Each differential codebook further contains additional codewords that are symmetric about the center location and that are each separated from the codebook center by a separation distance, as has also been described. Each differential codebook has its own unique separation distance. In other words, the separation distance for each one of the plurality of differential codebooks is different from the separation distance for each other one of the plurality of differential codebooks. In certain embodiments, for each one of the plurality of differential codebooks the additional codewords are equidistant from each other codeword in that codebook.

For complexity reduction, one entry of each column of each codeword may be converted to a real number. For example, the first row of the codeword can be converted to positive numbers or to zero by subtracting the global phase of each column. For Grassmannian codebook whose codewords are sub-planes or lines in the Grassmannian manifold, the storage and computational complexity may be further reduced. The codeword matrix may be converted to the one that has a triangle of zeros at one of the four corners of the codeword matrix, as illustrated in FIG. 4.

FIG. 5 is a flowchart illustrating a method 500 of reducing a quantization error in a MIMO beamforming system for a wireless network according to an embodiment of the invention.

A step 510 of method 500 is to define a differential codebook comprising a codebook center, a plurality of codewords, [e₁ . . . e_(N) _(s) ] G as a center location of the plurality of codewords, and additional codewords that are symmetric about the center location and that are each separated from the codebook center by a separation distance. As an example, the differential codebook can be similar to one or more of differential codebooks 100, 200, and 300 that are shown, respectively, in FIGS. 1, 2, and 3.

A step 520 of method 500 is to constrain the separation distance to be less than a predetermined limit. In one embodiment, the predetermined limit can be 15 or 20 degrees that is the angle between the center and any outer codeword.

Although the invention has been described with reference to specific embodiments, it will be understood by those skilled in the art that various changes may be made without departing from the spirit or scope of the invention. Accordingly, the disclosure of embodiments of the invention is intended to be illustrative of the scope of the invention and is not intended to be limiting. It is intended that the scope of the invention shall be limited only to the extent required by the appended claims. For example, to one of ordinary skill in the art, it will be readily apparent that the differential codebook and the related structures and methods discussed herein may be implemented in a variety of embodiments, and that the foregoing discussion of certain of these embodiments does not necessarily represent a complete description of all possible embodiments.

Additionally, benefits, other advantages, and solutions to problems have been described with regard to specific embodiments. The benefits, advantages, solutions to problems, and any element or elements that may cause any benefit, advantage, or solution to occur or become more pronounced, however, are not to be construed as critical, required, or essential features or elements of any or all of the claims.

Moreover, embodiments and limitations disclosed herein are not dedicated to the public under the doctrine of dedication if the embodiments and/or limitations: (1) are not expressly claimed in the claims; and (2) are or are potentially equivalents of express elements and/or limitations in the claims under the doctrine of equivalents. 

1. A differential codebook for a wireless network, the differential codebook comprising: a plurality of codewords; and [e₁ . . . e_(N) _(s) ] G as a center location of the plurality of codewords, where e_(k) represents a column vector comprising a plurality of rows including a k-th row and in which an entry on the k-th row is one and entries on each of the plurality of rows except for the k-th row are zero, G is any N_(s) by N_(s) unitary matrix including the identity matrix, and N_(s), represents a number of spatial streams in the wireless network, wherein: at least two of the plurality of codewords are symmetric about the center location.
 2. The differential codebook of claim 1 wherein: one of the plurality of codewords is at the center location.
 3. The differential codebook of claim 2 wherein: the plurality of codewords are equidistant from the center location.
 4. The differential codebook of claim 3 wherein: the plurality of codewords are equidistant from each other.
 5. The differential codebook of claim 1 wherein: no codeword is at the center location.
 6. The differential codebook of claim 5 wherein: the plurality of codewords are equidistant from the center location.
 7. The differential codebook of claim 6 wherein: the plurality of codewords are equidistant from each other.
 8. The differential codebook of claim 1 wherein: at least one entry of each column of the codewords is a real number.
 9. A MIMO beamforming system for a wireless network, the MIMO beamforming system comprising: a plurality of differential codebooks, each of which: has a codebook center and a plurality of codewords; contains [e₁ . . . e_(N) _(s) ] G as a center location of the plurality of codewords, where e_(k) represents a column vector comprising a plurality of rows including a k-th row and in which an entry on the k-th row is one and entries on each of the plurality of rows except for the k-th row are zero, G is any N_(s) by N_(s) unitary matrix including the identity matrix, and N_(s), represents a number of spatial streams in the wireless network; and contains at least two codewords that are symmetric about the center location and that are each separated from the codebook center by a separation distance, wherein: the separation distance for each one of the plurality of differential codebooks is different from the separation distance for each other one of the plurality of differential codebooks.
 10. The MIMO beamforming system of claim 9 wherein: for each one of the plurality of differential codebooks, one of the codewords is at the codebook center.
 11. The MIMO beamforming system of claim 10 wherein: for each one of the plurality of differential codebooks, the plurality of codewords are equidistant from each other.
 12. The MIMO beamforming system of claim 9 wherein: no codeword is at a center of any of the plurality of differential codebooks.
 13. The MIMO beamforming system of claim 12 wherein: for each one of the plurality of differential codebooks, the plurality of codewords are equidistant from each other.
 14. The MIMO beamforming system of claim 9 wherein: for each one of the plurality of differential codebooks, at least one entry of each column of the codewords is a real number.
 15. A method of reducing a quantization error in a MIMO beamforming system for a wireless network, the method comprising: defining a differential codebook comprising: a codebook center and a plurality of codewords; [e₁ . . . e_(N) _(s) ] G as a center location of the plurality of codewords, where e_(k) represents a column vector comprising a plurality of rows including a k-th row and in which an entry on the k-th row is one and entries on each of the plurality of rows except for the k-th row are zero, G is any N_(s) by N_(s) unitary matrix including the identity matrix, and N_(s), represents a number of spatial streams in the wireless network; and at least two codewords that are symmetric about the center location and that are each separated from the codebook center by a separation distance; and constraining the separation distance to be less than a predetermined limit.
 16. The method of claim 15 wherein: the predetermined limit is 20 degrees.
 17. The method of claim 15 wherein: at least one entry of each column of the codewords is a real number.
 18. The method of claim 15 wherein: one of the codewords is at the center location of the differential codebook; and the plurality of codewords are equidistant from each other.
 19. The method of claim 15 wherein: no codeword is at the center location; and the plurality of codewords are equidistant from each other. 